PrISM.jl : Introduction
Structure
All the models are a subtype of the abstract type AbstractGeophyModel, and their corresponding responses, outputs of the forward calls, are subtypes of the abstract type AbstractGeophyResponse.
The current framework provides a few models :
Each of these model types has a parameter m, that specifies the physical property of the medium the method is sensitive to, e.g., electrical resistivity for magnetotelluric MTModel and shear wave velocity for Rayleigh waves RWModel. This is the parameter that is natively inverted for in the inversion schemes provided in the package. Each model type also has a parameter h that defines the grid-size. In 1D, this corresponds to layer thicknesses. Some models such as RWModel also require P-wave velocities and densities alongside the usual parameters. These are again constant parameters, and not inverted for.
Modeling
Calculation of forward responses can be done by calling the forward function on the corresponding geophysics models, along with the necessary survey specifications, e.g., frequencies for MTModel and RWModel. Specific pages for the models provide an introduction along with example to demonstrate forward calls.
Initial parameters
Some geophysical models also require parameters that are essential for the numerical recipes of the forward models. While we provide default values for these models, you can easily change these values. Surface wave models are a good example of this, and the user is recommended the corresponding introduction pages (Rayleigh waves, Love waves).
Bounds transformation
The objective of geophysical inversion is to obtain estimates of the physical properties. The geophysical inversion, being ill-posed, can be very unstable and highly challenging. The most common strategy is to perform inversion in a space that is constrained so that the inversion scheme does not assume any unrealistic values. An intuitive example is using log-space for electrical resistivities. Since the electrical resistivity in the subsurface spans orders of magnitude, the inversion is well-behaved in the log-space. Moreover, the guarantee that the electrical resistivity will always be positive comes for free.
You may want to further constrain this space, e.g., the shear wave velocities should be between 3 and 4.5
Mutating operations
We provide mutating versions of the forward calls as well. These functions allocate less memory and, therefore, are more efficient. The forward calls of the geophysical methods are reasonably computational and there is not much speedup obtained because of these mutations.